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From the jungle to the garden : growing trees for Markov chain Monte Carlo inference in undirected graphical models Rivasseau, Jean-Noël

Abstract

In machine-learning, Markov Chain Monte Carlo (MCMC) strategies such as Gibbs sampling are important approximate inference techniques. They use a Markov Chain mechanism to explore and sample the state space of a target distribution. The generated samples are then used to approximate the target distribution. MCMC is mathematically guaranteed to converge with enough samples. Yet some complex graphical models can cause it to converge very slowly to the true distribution of interest. Improving the quality and efficiency of MCMC methods is an active topic of research in the probabilistic graphical models field. One possible method is to "block" some parts of the graph together, sampling groups of variables instead of single variables. In this thesis, we concentrate on a particular blocking scheme known as tree sampling. Tree sampling operates on groups of trees, and as such requires that the graph be partitioned in a special way prior to inference. We present new algorithms to find tree partitions on arbitrary graphs. This allows tree sampling to be used on any undirected probabilistic graphical model.

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